{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Supervised Learning (Regression)\n",
    "\n",
    "In supervised learning, the task is to infer hidden structure from\n",
    "labeled data, comprised of training examples $\\{(x_n, y_n)\\}$.\n",
    "Regression typically means the output $y$ takes continuous values.\n",
    "\n",
    "We demonstrate with an example in Edward. A webpage version is available at\n",
    "http://edwardlib.org/tutorials/supervised-regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from __future__ import absolute_import\n",
    "from __future__ import division\n",
    "from __future__ import print_function\n",
    "\n",
    "import edward as ed\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "\n",
    "from edward.models import Normal\n",
    "\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data\n",
    "\n",
    "Simulate training and test sets of $40$ data points. They comprise of\n",
    "pairs of inputs $\\mathbf{x}_n\\in\\mathbb{R}^{10}$ and outputs\n",
    "$y_n\\in\\mathbb{R}$. They have a linear dependence with normally\n",
    "distributed noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def build_toy_dataset(N, w):\n",
    "  D = len(w)\n",
    "  x = np.random.normal(0.0, 2.0, size=(N, D))\n",
    "  y = np.dot(x, w) + np.random.normal(0.0, 0.01, size=N)\n",
    "  return x, y\n",
    "\n",
    "\n",
    "ed.set_seed(42)\n",
    "\n",
    "N = 40  # number of data points\n",
    "D = 10  # number of features\n",
    "\n",
    "w_true = np.random.randn(D) * 0.5\n",
    "X_train, y_train = build_toy_dataset(N, w_true)\n",
    "X_test, y_test = build_toy_dataset(N, w_true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model\n",
    "\n",
    "Posit the model as Bayesian linear regression (Murphy, 2012).\n",
    "It assumes a linear relationship between the inputs\n",
    "$\\mathbf{x}\\in\\mathbb{R}^D$ and the outputs $y\\in\\mathbb{R}$.\n",
    "\n",
    "For a set of $N$ data points $(\\mathbf{X},\\mathbf{y})=\\{(\\mathbf{x}_n, y_n)\\}$,\n",
    "the model posits the following distributions:\n",
    "\n",
    "\\begin{align*}\n",
    "  p(\\mathbf{w})\n",
    "  &=\n",
    "  \\text{Normal}(\\mathbf{w} \\mid \\mathbf{0}, \\sigma_w^2\\mathbf{I}),\n",
    "  \\\\[1.5ex]\n",
    "  p(b)\n",
    "  &=\n",
    "  \\text{Normal}(b \\mid 0, \\sigma_b^2),\n",
    "  \\\\\n",
    "  p(\\mathbf{y} \\mid \\mathbf{w}, b, \\mathbf{X})\n",
    "  &=\n",
    "  \\prod_{n=1}^N\n",
    "  \\text{Normal}(y_n \\mid \\mathbf{x}_n^\\top\\mathbf{w} + b, \\sigma_y^2).\n",
    "\\end{align*}\n",
    "\n",
    "The latent variables are the linear model's weights $\\mathbf{w}$ and\n",
    "intercept $b$, also known as the bias.\n",
    "Assume $\\sigma_w^2,\\sigma_b^2$ are known prior variances and $\\sigma_y^2$ is a\n",
    "known likelihood variance. The mean of the likelihood is given by a\n",
    "linear transformation of the inputs $\\mathbf{x}_n$.\n",
    "\n",
    "Let's build the model in Edward, fixing $\\sigma_w,\\sigma_b,\\sigma_y=1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = tf.placeholder(tf.float32, [N, D])\n",
    "w = Normal(loc=tf.zeros(D), scale=tf.ones(D))\n",
    "b = Normal(loc=tf.zeros(1), scale=tf.ones(1))\n",
    "y = Normal(loc=ed.dot(X, w) + b, scale=tf.ones(N))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we define a placeholder `X`. During inference, we pass in\n",
    "the value for this placeholder according to data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inference\n",
    "\n",
    "We now turn to inferring the posterior using variational inference.\n",
    "Define the variational model to be a fully factorized normal across\n",
    "the weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "qw = Normal(loc=tf.get_variable(\"qw/loc\", [D]),\n",
    "            scale=tf.nn.softplus(tf.get_variable(\"qw/scale\", [D])))\n",
    "qb = Normal(loc=tf.get_variable(\"qb/loc\", [1]),\n",
    "            scale=tf.nn.softplus(tf.get_variable(\"qb/scale\", [1])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run variational inference with the Kullback-Leibler divergence, using \n",
    "$250$ iterations and $5$ latent variable samples in the algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 66.347\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\n"
     ]
    }
   ],
   "source": [
    "inference = ed.KLqp({w: qw, b: qb}, data={X: X_train, y: y_train})\n",
    "inference.run(n_samples=5, n_iter=250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case `KLqp` defaults to minimizing the\n",
    "$\\text{KL}(q\\|p)$ divergence measure using the reparameterization\n",
    "gradient.\n",
    "For more details on inference, see the [$\\text{KL}(q\\|p)$ tutorial](http://edwardlib.org/tutorials/klqp)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Criticism\n",
    "\n",
    "A standard evaluation for regression is to compare prediction accuracy on\n",
    "held-out \"testing\" data. We do this by first forming the posterior predictive\n",
    "distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_post = ed.copy(y, {w: qw, b: qb})\n",
    "# This is equivalent to\n",
    "# y_post = Normal(loc=ed.dot(X, qw) + qb, scale=tf.ones(N))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this we can evaluate various quantities using predictions from\n",
    "the model (posterior predictive)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean squared error on test data:\n",
      "0.0480191\n",
      "Mean absolute error on test data:\n",
      "0.187246\n"
     ]
    }
   ],
   "source": [
    "print(\"Mean squared error on test data:\")\n",
    "print(ed.evaluate('mean_squared_error', data={X: X_test, y_post: y_test}))\n",
    "\n",
    "print(\"Mean absolute error on test data:\")\n",
    "print(ed.evaluate('mean_absolute_error', data={X: X_test, y_post: y_test}))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The trained model makes predictions with low error\n",
    "(relative to the magnitude of the output).\n",
    "\n",
    "We can also visualize the fit by comparing data generated with the\n",
    "prior to data generated with the posterior (on the first feature\n",
    "dimension)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def visualise(X_data, y_data, w, b, n_samples=10):\n",
    "  w_samples = w.sample(n_samples)[:, 0].eval()\n",
    "  b_samples = b.sample(n_samples).eval()\n",
    "  plt.scatter(X_data[:, 0], y_data)\n",
    "  plt.ylim([-10, 10])\n",
    "  inputs = np.linspace(-8, 8, num=400)\n",
    "  for ns in range(n_samples):\n",
    "    output = inputs * w_samples[ns] + b_samples[ns]\n",
    "    plt.plot(inputs, output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAe0AAAFMCAYAAADm9OSwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJaS0hRBCiCjxfxsQCN2nooXRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18e198ddc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize samples from the prior.\n",
    "visualise(X_train, y_train, w, b, n_samples=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAe0AAAFMCAYAAADm9OSwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTGJfju0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18e197c96a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize samples from the posterior.\n",
    "visualise(X_train, y_train, qw, qb, n_samples=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model has learned a linear relationship between the\n",
    "first dimension of $\\mathbf{x}\\in\\mathbb{R}^D$ and the outputs\n",
    "$y\\in\\mathbb{R}$."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
